Classification of minimal Frobenius hypermaps

Kai Yuan, Yan Wang

Abstract


In this paper, we give a classification of orientably regular hypermaps with an automorphism group that is a minimal Frobenius group. A Frobenius group G is called minimal if it has no nontrivial normal subgroup N such that G/N is a Frobenius group. An orientably regular hypermap H is called a Frobenius hypermap if Aut(H) acting on the hyperfaces is a Frobenius group. A minimal Frobenius hypermap is a Frobenius hypermap whose automorphism group is a minimal Frobenius group with cyclic point stabilizers. Every Frobenius hypermap covers a minimal Frobenius hypermap. The main theorem of this paper generalizes the main result of Breda D’Azevedo and Fernandes (Eur. J. Comb. 32: 233–242, 2011).

Keywords


Frobenius hypermap, Frobenius group

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DOI: https://doi.org/10.26493/1855-3974.2415.fd1

ISSN: 1855-3974

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